Finite Group Databasebeta

← #38734664

Subgroups — #38734664

Order 24896.

334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20261965C211yesmaximal, characteristic, complemented
2C22×C22⋊D389C211yesmaximal, characteristic, complemented
3#27159380C212yesmaximal, complemented
4#27159370C212yesmaximal, complemented
5#27159357C212yesmaximal, complemented
6#27159356C212yesmaximal, complemented
7#27159354C211yesmaximal, characteristic, complemented
8#27159353C211yesmaximal, characteristic, complemented
9#27159352C211yesmaximal, characteristic, complemented
10#27159340C211yesmaximal, characteristic, complemented
11#120×C389C211yesmaximal, characteristic, complemented
12C23×D389C2211yescharacteristic
13#20261965—24no—
14C2×Dic778C2211yescharacteristic, complemented
15C2×D1556C2212yescomplemented
16C2×C22⋊D389—24no—
17C2×C22⋊D389C2211yescharacteristic
18C2×C22⋊D389C2212yes—
19C2×C22⋊D389C2212yes—
20C2×C22⋊D389C2211yescharacteristic, complemented
21C2×C22⋊D389C2212yescomplemented
22C2×C22⋊D389C2212yescomplemented
23C22×Dic389C2211yescharacteristic
24C22×Dic389C2211yescharacteristic, complemented
25C2×C4×D389C2211yescharacteristic, complemented
26#20261945C2212yescomplemented
27C22⋊Dic389C2211yescharacteristic
28C22⋊Dic389C2212yescomplemented
29#20261943C2212yescomplemented
30#20261943C2212yescomplemented
31C4×Dic389C2212yescomplemented
32C24×C389C2211yescharacteristic
33C2×D4×C389C2211yescharacteristic
34C2×D4×C389C2212yescomplemented
35C22⋊C4×C389C2211yescharacteristic
36C22⋊C4×C389C2212yescomplemented
37C22×D389—22no—
38C22×D389—42no—
39C22×D389C2312yes—
40C22×D389C2311yescharacteristic
41Dic778—22no—
42D1556—42no—
43C22⋊D389—22no—
44C22⋊D389—24no—
45C22⋊D389—24no—
46C22⋊D389—22no—
47C22⋊D389—42no—
48C22⋊D389—42no—
49C2×Dic389—22no—
50C2×Dic389D414yescomplemented
51C2×Dic389C2312yes—
52C2×Dic389C2311yescharacteristic
53C2×Dic389C2311yescharacteristic
54C2×Dic389C2311yescharacteristic
55C4×D389—22no—
56C23×C389—22no—
57C23×C389—42no—
58C23×C389C2312yes—
59C23×C389C2311yescharacteristic
60C23×C389C2311yescharacteristic
61D4×C389—22no—
62D4×C389—42no—
63C2×C4×C389C2312yes—
64C2×C4×C389C2311yescharacteristic
65C22×C389—22no—
66C22×C389—22no—
67C22×C389—21no—
68C22×C389—22no—
69C22×C389—22no—
70C22×C389—22no—
71C22×C389—44no—
72C22×C389C2×D412yes—
73C22×C389C2411yescharacteristic
74C2×D389—22no—
75C2×D389—21no—
76C2×D389—22no—
77C2×D389—22no—
78C2×D389—22no—
79C2×D389—44no—
80C4×C389—21no—
81C4×C389—22no—
82Dic389—21no—
83Dic389—22no—
84Dic389C2×D412yes—
85Dic389C2×D412yes—
86C2×C389—22no—
87C2×C389—41no—
88C2×C389—42no—
89C2×C389C22×D411yescharacteristic
90C2×C389H(5,𝔽2)12yes—
91D389—41no—
92D389—42no—
93C389#53511yescharacteristic, complemented, Sylow
94#535—3891nomaximal, Sylow
95C2×#41—3891no—
96C22×D4—3891no—
97#127—3892no—
98#124—3892no—
99#121—3892no—
100#121—3892no—
101#120—3891no—
102#120—3891no—
103#120—3891no—
104#120D38911yescharacteristic, complemented
105#117—3891no—
106C24—3891no—
107C24C2×D38911yescharacteristic
108#41—7784no—
109C2×Q8—3891no—
110C2×D4—7784no—
111C2×D4—3891no—
112C2×D4—3892no—
113C2×D4—3892no—
114C2×D4—3891no—
115C2×D4—3892no—
116C2×D4—3892no—
117C2×D4—3892no—
118C2×D4C2×D38911yescharacteristic
119C2×D4C2×D38912yescomplemented
120C22×C4—3891no—
121C22×C4—3891no—
122C22×C4—3891no—
123C4⋊C4—3892no—
124C22⋊C4—3891no—
125C22⋊C4—3892no—
126C22⋊C4—3892no—
127C22⋊C4—3892no—
128C22⋊C4C2×D38911yescharacteristic
129C22⋊C4C2×D38912yescomplemented
130C42—3892no—
131C23—22no—
132C23—42no—
133C23—7782no—
134C23—15562no—
135C23—3892no—
136C23—3891no—
137C23C22×D38912yes—
138C23C22×D38911yescharacteristic
139C23C22×D38911yescharacteristic
140Q8—7782no—
141D4—22no—
142D4—42no—
143D4—7782no—
144D4—7784no—
145D4—7784no—
146D4—7782no—
147D4—15562no—
148D4—15562no—
149D4—15562no—
150C2×C4—7782no—
151C2×C4—7782no—
152C2×C4—3892no—
153C2×C4—3891no—
154C2×C4—3894no—
155C2×C4—3891no—
156C2×C4—3891no—
157C2×C4C22×D38912yes—
158C2×C4C22×D38911yescharacteristic
159C22—22no—
160C22—21no—
161C22—22no—
162C22—22no—
163C22—22no—
164C22—22no—
165C22—44no—
166C22—7781no—
167C22—7782no—
168C22—7782no—
169C22—7782no—
170C22—7782no—
171C22—15564no—
172C22D4×D38912yes—
173C22C23×D38911yescharacteristic
174C4—21no—
175C4—22no—
176C4—7781no—
177C4—7782no—
178C4—3892no—
179C4—3892no—
180C2—22no—
181C2—42no—
182C2—41no—
183C2—15562no—
184C2—15561no—
185C2C2×D4×D38911yescharacteristic
186C2#2715942912yes—
subgroupG/H
center, FrattiniC22C23×D389
commutator, socle, cosocleC22×C389C24
Fitting#120×C389C2
hypercenter#120D389
hypocenterC389#535
LCSG ▷ C22×C389 ▷ C389
UCSC1 ◁ C22 ◁ #120

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#20261965C2semidirect
2. C22×C22⋊D389C2semidirect
3. #27159380C2semidirect
4. #27159370C2semidirect
5. #27159357C2semidirect
6. #27159356C2semidirect
7. #27159354C2semidirect
8. #27159353C2semidirect
9. #27159352C2semidirect
10. #27159340C2semidirect
11. #120×C389C2semidirect
14. C2×Dic778C22semidirect
15. C2×D1556C22semidirect
20. C2×C22⋊D389C22semidirect
21. C2×C22⋊D389C22semidirect
22. C2×C22⋊D389C22semidirect
24. C22×Dic389C22semidirect
25. C2×C4×D389C22semidirect
26. #20261945C22semidirect
28. C22⋊Dic389C22semidirect
29. #20261943C22semidirect
30. #20261943C22semidirect
31. C4×Dic389C22semidirect
34. C2×D4×C389C22semidirect
36. C22⋊C4×C389C22semidirect
50. C2×Dic389D4semidirect
93. C389#535semidirect
104. #120D389semidirect
119. C2×D4C2×D389semidirect
129. C22⋊C4C2×D389semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#202619652
C22×C22⋊D3892
#271593802
#271593702
#271593572
#271593562
#271593542
#271593532
#271593522
#271593402
#120×C3892
#535389